National Taiwan University Dept MathCheng, Ming-YenMing-YenChengHall, PeterPeterHall2006-09-272018-06-282006-09-272018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/20060927121126023390In a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to e±- ciency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, medicine, meteorology or geol- ogy. We suggest a tracking-based method for estimating a support boundary when it is composed of a ¯nite number of smooth curves, meeting together at corners. The smooth parts of the boundary are assumed to have continuously turning tan- gents & bounded curvature, & the corners are not allowed to be in¯nitely sharp; that is, the angle between the two tangents should not equal ¼. In other respects, however, the boundary may be quite general. In particular it need not be uniquely de¯ned in Cartesian coordinates, its corners my be either concave or convex, and its smooth parts may be neither concave nor convex. Tracking methods are well suited to such generalities, & they also have the advantage of requiring relatively small amounts of computation. It is shown that they achieve optimal convergence rates, in the sense of uniform approximation.application/pdf291323 bytesapplication/pdfzh-TWBandwidthboundarycornercurvaturefrontierkernel methodlocal linearnonparametric curve estimationsupportjournal articlehttp://ntur.lib.ntu.edu.tw/bitstream/246246/20060927121126023390/1/ch-track2.pdf